PARIS—French President Emmanuel Macron won a commanding majority in parliamentary elections, empowering him to carry out economic overhauls that are contentious at home but pivotal in persuading Germany and the European Union to insulate the common currency from shocks.

Mr. Macron’s party, La République en Marche, and its centrist ally had won 350 of the 577 seats in the National Assembly in the second and final round of voting on...